johncarlosbaez

johncarlosbaez, 5 hours ago (edited 4 hours ago) to random

Robert Recorde introduced the equal sign in 1557. He used parallel lines because "no two things can be more equal". And his equal sign was hilariously looooooong.

This is from @mjd's excellent blog article:

https://blog.plover.com/math/recorde.html

and I recommend following him here on Mastodon.

It's fun to fight your way through Recorde's text, with its old font and spellings. But if you give up, @mjd has transliterated it:

Howbeit, for easie alteration of equations. I will propounde a fewe exanples, bicause the extraction of their rootes, maie the more aptly bee wroughte. And to avoide the tediouse repetition of these woordes "is equalle to" I will sette as I doe often in woorke use, a pair of paralleles, or Gemowe lines of one lengthe, thus: =====, bicause noe 2 thynges, can be moare equalle.

The only real mystery here is "Gemowe", which means "identical" and comes from the same root as "Gemini": twins.

In the same book Robert Recorde introduced the mathematical term "zenzizenzizenzike", but I'm afraid for that you'll have to read @mjd's article!

mjd, 14 hours ago to random

This is the world's first use of the modern equals sign, from Robert Recorde's 1557 book The Whetstone of Witte.

(Screencap from Internet Archive's scan of the book: https://archive.org/details/TheWhetstoneOfWitte/page/n237/mode/2up)

(I also wrote a blog post a couple of years back explaining what it says if you are interested: https://blog.plover.com/math/recorde.html)

highergeometer, 1 day ago to random

Two thematically related papers

Felix Cherubini, Thierry Coquand, Matthias Hutzler, David Wärn, "Projective Space in Synthetic Algebraic Geometry"

Abstract: Working in an abstract, homotopy type theory based axiomatization of the higher Zariski-topos called synthetic algebraic geometry, we show that the Picard group of projective n-space is the integers, the automorphism group of projective n-space is PGL(n+1) and morphisms between projective standard spaces are given by homogenous polynomials in the usual way.

https://arxiv.org/abs/2405.13916

=====

Matías Menni, "Bi-directional models of `Radically Synthetic' Differential Geometry", Theory and Applications of Categories, Vol. 40, 2024, No. 15, pp 413-429.

Abstract: The radically synthetic foundation for smooth geometry formulated in [Law11] postulates a space T with the property that it has a unique point and, out of the monoid T^T of endomorphisms, it extracts a submonoid R which, in many cases, is the (commutative) multiplication of a rig structure. The rig R is said to be bi-directional if its subobject of invertible elements has two connected components. In this case, R may be equipped with a pre-order compatible with the rig structure. We adjust the construction of `well-adapted' models of Synthetic Differential Geometry in order to build the first pre-cohesive toposes with a bi-directional R. We also show that, in one of these pre-cohesive variants, the pre-order on R, derived radically synthetically from bi-directionality, coincides with that defined in the original model.
http://www.tac.mta.ca/tac/volumes/40/15/40-15abs.html